Triage: Which Inferential Stats Case Should I Use?

Summary:
How do you know which hypothesis test or confidence
interval to use? This page leads you through a series of decisions
to a specific numbered case, cross referenced to
Inferential Statistics Cases.

The interactive version is much easier
to use. Please visit https://BrownMath.com/stat/castriag.htm.

If you print this page, it will appear
in a more compact form but you’ll lose the interactivity.

Node 110. Numeric data, pop. mean(s)

How many samples or populations are there?

One — This includes the case where you have a fixed reference point in a different population. Example: “In 1990 the mean household income was $39,045. A recent survey of 500 households found a mean of. ...” The recent survey is a sample, but the 1990 value is not a sample, just a number to test against. — go to Node 120

Two, paired data — go to Case 3Caution: In paired data, you get two numbers from each
individual or from each “team” (twins, husband/wife, etc.)

Two, unpaired data — go to Case 4Caution: In unpaired data, you have two unrelated groups,
and you get one number from each person in each group.

Three or more — go to Case 8Requirements: 1. Samples are independent. 2. Data are
normally distributed. 3. All populations have same σ.
(The test is robust, so moderate departures from requirements 2 and 3
are okay, especially if sample sizes are equal or nearly equal.)

Node 120. Numeric data, one pop. mean

Yes — go to Case 0Caution: Do you really know the standard deviation of
the population? When “a survey found a mean of 800 and a
standard deviation of 45”, that’s a sample standard
deviation just like it’s a sample mean.

Node 150. Numeric
data, pop. standard deviation(s) or variance(s)

How many populations are there?

One — go to Case 1SRequirement: Population must be normally distributed, not
just roughly normal.

Two — go to Case 4SRequirements: 1. Samples are independent.
2. Populations must be normally distributed, not
just roughly normal.

Node 200. Binomial (yes/no) data

How many samples or populations are there?

One — go to Case 2Caution: This includes the case where you have a fixed
reference point in a different population. Example: “In 1990,
68% of Americans felt pessimistic about their financial future. A
recent survey of 1500 Americans found that 1089 of
them. ...” The recent survey is a sample, but the 1990
value is not a sample, just a number to test against.

Node 300. Categorical data

Node 350. Categorical
data for one population

How many variables are there?

One — go to Case 6Here you have one row or column of numbers, representing the
number of individuals with each value of the trait. For example, if
the trait is hair color then you would have an observed number of
blonds, an observed number of brunets, an observed number of redheads,
and so on. You test that against a model of expected percentages or
ratios.

Two — go to Case 7 (independence)
Here you have a two-way table of one population. The rows
represent levels of one trait, such as educational level, and the
columns represent a second trait, such as marital status.